THE JARROW AND TURNBULL SETTING REVISITED

Abstract

We consider a financial market with zero-coupon bonds that are exposed to credit and liquidity risk. We revisit the famous Jarrow & Turnbull (1995) setting in order to account for these two intricately intertwined risk types. We utilize the foreign exchange analogy that interprets defaultable zero-coupon bonds as a conversion of nondefaultable foreign counterparts. The relevant exchange rate is only partially observable in the market filtration, which leads us naturally to an application of the concept of platonic financial markets as introduced by Cuchiero et al. (2020). We provide an example of tractable term structure models that are driven by a two-dimensional affine jump diffusion. Furthermore, we derive explicit valuation formulae for marketable products, e.g. for credit default swaps.